MWC 656 is the first known Be/black hole (BH) binary system. Be/BH binaries are important in the context of binary system evolution and sources of detectable gravitational waves because they are possible precursors of coalescing neutron star/BH binaries. X-ray observations conducted in 2013 revealed that MWC 656 is a quiescent high-mass X-ray binary (HMXB), opening the possibility to explore X-ray/radio correlations and the accretion/ejection coupling down to low luminosities for BH HMXBs. Here we report on a deep joint Chandra/VLA observation of MWC 656 (and contemporaneous optical data) conducted in 2015 July that has allowed us to unambiguously identify the X-ray counterpart of the source. The X-ray spectrum can be fitted with a power law with Γ ∼ 2, providing a flux of ≃4 × 10‑15 erg cm‑2 s‑1 in the 0.5–8 keV energy range and a luminosity of L X ≃ 3 × 1030 erg s‑1 at a 2.6 kpc distance. For a 5 M⊙ BH this translates into ≃5 × 10‑9 L Edd. These results imply that MWC 656 is about 7 times fainter in X-rays than it was two years before and reaches the faintest X-ray luminosities ever detected in stellar-mass BHs. The radio data provide a detection with a peak flux density of 3.5 ± 1.1 μJy beam‑1. The obtained X-ray/radio luminosities for this quiescent BH HMXB are fully compatible with those of the X-ray/radio correlations derived from quiescent BH low-mass X-ray binaries. These results show that the accretion/ejection coupling in stellar-mass BHs is independent of the nature of the donor star.